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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 367 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  2. 2.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 115 (c) 106 (d) 124
  3. 3.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 153 (c) 54 (d) 51
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 14 (d) 15
  5. 5.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  6. 6.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 27 (c) 24 (d) 8
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 17 (d) 18
  9. 9.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 324 (c) 379 (d) 369
  10. 10.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 33 (c) 42 (d) 24
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  12. 12.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 45 (c) 126 (d) 42
  13. 13.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 17 (d) 6
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 18 (d) 16
  17. 17.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 574 (c) 564 (d) 454
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  19. 19.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 7 (d) 24
  20. 20.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 60 (c) 19 (d) 171
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 7 (d) 5
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 10 (b) 8 (c) 13 (d) 12
  23. 23.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 132 (d) 114
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17
  25. 25.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 36 (d) 99
  26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 39 (d) 36
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  28. 28.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 174 (c) 192 (d) 184
  29. 29.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
  30. 30.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 537 (c) 436 (d) 546
  31. 31.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 297 (c) 288 (d) 270
  32. 32.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 190 (c) 198 (d) 180
  33. 33.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 5 (c) 45 (d) 18
  34. 34.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 411 (d) 346
  35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 14 (d) 15
  36. 36.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 237 (c) 230 (d) 238
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 20
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 66 (c) 189 (d) 21

Answer key

  1. 18
  2. 115
  3. 51
  4. 15
  5. 2
  6. 24
  7. 19
  8. 18
  9. 378
  10. 33
  11. 18
  12. 42
  13. 27
  14. 9
  15. 17
  16. 17
  17. 573
  18. 9
  19. 21
  20. 57
  21. 6
  22. 12
  23. 123
  24. 16
  25. 33
  26. 36
  27. 8
  28. 183
  29. 30
  30. 546
  31. 297
  32. 189
  33. 15
  34. 411
  35. 15
  36. 237
  37. 19
  38. 4
  39. 4
  40. 63

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